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# Approximation theory

Approximation theory is concerned with approximating functions of a given class, or data of a given type, using functions from another, usually more elementary, class. A simple example is the problem of approximating a function such as ex by means of polynomial functions. The efficient solution of such problems is of great importance for computing such approximations, and this module will introduce the mathematical theory behind many approximation methods in common use. This intermediate-level module is based on the set book Approximation Theory and Methods by M. J. D. Powell.

## Qualifications

M832 is an optional module in our:

This module can also count towards M03, which is no longer available to new students.

## Module

Module code
M832
Credits

Credits

• Credits measure the student workload required for the successful completion of a module or qualification.
• One credit represents about 10 hours of study over the duration of the course.
• You are awarded credits after you have successfully completed a module.
• For example, if you study a 60-credit module and successfully pass it, you will be awarded 60 credits.
30
Study level
To enable you to make international comparisons, the information provided shows how OU postgraduate modules correspond to the Framework for Higher Education Qualifications in England, Northern Ireland and Wales (FHEQ).
Study method
Distance learning
Find out more in Why the OU?
Module cost
See Module registration
Entry requirements

Find out more about entry requirements.

## What you will study

The subject of approximation theory lies at the frontier between applied mathematics and pure mathematics. Practical problems, such as the computer calculation of special functions like ex, lead naturally to theoretical problems, such as ‘how well can we approximate by a given method?’ or ‘how fast does a given algorithm converge?’.

The module is based on Approximation Theory and Methods by M. J. D. Powell (Cambridge University Press, 1981). This book provides an excellent introduction to these theoretical problems, covering the basic theory of a wide range of approximation methods

### You will learn

Successful study of this module should enhance your skills in understanding complex mathematical texts, constructing solutions to problems logically and communicating mathematical ideas clearly.

Note you must study this module if you wish to take the 'Advances in approximation theory' topic for your Dissertation in mathematics (M840).

## Teaching and assessment

• Marking your assignments (TMAs) and providing detailed feedback for you to improve.
• Guiding you to additional learning resources.
• Providing individual guidance, whether that’s for general study skills or specific module content.
• Facilitating online discussions between your fellow students, in the dedicated module and tutor group forums.

Module tutors also run online tutorials throughout the module. Where possible, recordings of online tutorials will be made available to students. While these tutorials won’t be compulsory for you to complete the module, you’re strongly encouraged to take part. If you want to participate, you’ll likely need a headset with a microphone.

### Assessment

The assessment details can be found in the facts box above.

You will be expected to submit your tutor-marked assignments (TMAs) online using the eTMA system, unless there are some difficulties which prevent you from doing so. In these circumstances, you must negotiate with your tutor to get their agreement to submit your assignment on paper.

### Course work includes

 4 Tutor-marked assignments (TMAs) Examination No residential school

## Future availability

Approximation theory (M832) starts every other year – in October.

This page describes the module that started in October 2020. There’s no start in 2021; the next start will be in October 2022.

We expect it to start for the last time in October 2022.

## Regulations

As a student of The Open University, you should be aware of the content of the academic regulations which are available on our Student Policies and Regulations website.

## Entry requirements

To study this module you must declare the MSc in Mathematics (or another qualification towards which the module can count) as your qualification intention.

Normally, you should have also completed at least one of the entry modules for the MSc in Mathematics (F04), Calculus of variations and advanced calculus (M820) or Analytic number theory I (M823).

The subject of approximation theory lies at the frontier between applied mathematics and pure mathematics, since practical problems such as how to calculate special functions on a computer lead to theoretical problems such as 'which approximation method is best?'. Therefore you will need some familiarity with real analysis and linear algebra, such as that developed in typical undergraduate courses, and knowing the basic properties of metric spaces would also be useful.

All teaching is in English and your proficiency in the English language should be adequate for the level of study you wish to take. We strongly recommend that students have achieved an IELTS (International English Language Testing System) score of at least 7. To assess your English language skills in relation to your proposed studies you can visit the IELTS website.

## Register

Start End Fee
- - -

No current presentation - see Future availability

This module is expected to start for the last time in October 2022.

## Future availability

Approximation theory (M832) starts every other year – in October.

This page describes the module that started in October 2020. There’s no start in 2021; the next start will be in October 2022.

We expect it to start for the last time in October 2022.

### Study costs

There may be extra costs on top of the tuition fee, such as set books, a computer and internet access.

### Study weekend

This module has an optional study weekend. You must pay £60 for tuition and refreshments. You must also pay for your travel to and from the venue, and accommodation if you need it. Due to the ongoing pandemic, we may replace face-to-face events with online alternatives.

## Study materials

### What's included

• a week-by-week study planner
• course-specific module materials
• audio and video content
• assessment details and submission section
• online tutorial access

You'll be provided with printed materials covering the content of the module, including explanations, examples and activities to aid your understanding of the concepts and associated skills and techniques that are contained in the set book. You will need to obtain your own copy of the set book.

### You will need

A scientific calculator.

### Computing requirements

You'll need a desktop or laptop computer with an up-to-date version of 64-bit Windows 10 (note that Windows 7 is no longer supported) or macOS and broadband internet access.

To join in spoken conversations in tutorials we recommend a wired headset (headphones/earphones with a built-in microphone).

Our module websites comply with web standards and any modern browser is suitable for most activities.

Our OU Study mobile App will operate on all current, supported, versions of Android and iOS. It's not available on Kindle.

It's also possible to access some module materials on a mobile phone, tablet device or Chromebook, however, as you may be asked to install additional software or use certain applications, you'll also require a desktop or laptop as described above.